Yes it's Eldarion* but he also had 6 daughters with Arwen as well - there's not really much else to know about the kid. Tolkien kind of lost interest in it all for the Fourth Age after he killed off Sauron for the third time.

The immortality gig wore out with Arwen who died of grief and followed Aragorn into permanent peace outside the spheres of Arda (she didn't get to re-incarnate like proper Elves 'cos she chose to marry a mere mortal ) and their kids all lived happily ever after until they too kicked the bucket. All the Elves had sodded off into the West by then so nobody gave a damn....

*it means Son of the Elves apparently - both Arwen and Aragorn were descended from royal Elves - in fact she was his cousin several hundred times removed as he was descended from Elrond's twin brother Elros. Not a lot of people know that

"Some men see things as they are and ask why. Others dream things that never were and ask why not.” George Bernard Shaw

I only wish I could say more but there isn't anything to tell - the daughters thing isn't 'known' for sure but they had at least 2 and some afterthought writing mention the half dozen but he'd already repeated a lot of the names already (there are at least 2 Denethors and Boromirs and possibly another Legolas as well... ) so I guess he just didn't bother with naming the girls

"Some men see things as they are and ask why. Others dream things that never were and ask why not.” George Bernard Shaw

Thank you for the replies everyone, especially Jan Van Quirm. The missus only wanted to know the name of their son, so I could earn some brownie points here Guess I will know who to contact if I require any further Middle Earth education

No - sorry Cohen I don't and I doubt it's something anyone else would since there's a lot of sources out there now all based on the copious notes that Tolkien left and his son and archivist Christopher has collated.

There's reams of 'genealogical' info in Bk 12 of the History of Middle Earth, Peoples of Middle Earth on the Kings of Numenor, Arnor and Gondor which ends with Eldarion but I'm afraid he's the last and only child named after Aragorn. If you want a more accessible online source then I use Encyclopedia of Arda (Glyphweb) and the Wiki Middle Earth Portal for quick hits and for more in depth or practical info Tolkien Gateway which has v. useful stuff like timelines pre-LOTR as well as news of the forthcoming Hobbit films

"Some men see things as they are and ask why. Others dream things that never were and ask why not.” George Bernard Shaw